Leases are set up so that you get an initial bonus payment to sign the lease + a percentage of the overall production (less costs and a bunch of ther stuff) as a royalty for your minerals.
Leases typically last for 3 years. If the oil and gas company does not begin production during that time, the lease will lapse. Meaning another company, or the same company, will have to renew the lease for you and pay you that bonus payment again.
However, if they do drill a well and produce, the company does not have to pay you a new bonus payment at the end of the third year b/c they are paying you instead through the negotiated royalty amount. Therefore, when the third year is up but you have a producing well in your leased section, then that lease is "held under production".